PURPOSE What is the relationship between Pressure Difference and Flow Rate? What is the difference between Ohmic and Non-Ohmic materials?
HYPOTHESIS W/ RATIONALE The pressure difference and flow rate have a direct relationship. I believe this because Ohm's Law includes the equation V=IR. Ohmic materials will follow Ohm's law while non-ohmic materials will not.
PROCEDURE Available materials: variable power supply, batteries/holders, long bulb and socket, assorted resistors, multimeters, lead wires General Set-up: Measure voltage and current in circuit displayed below using multimeter and different resistors
DATA SAMPLE CALCULATIONS
R=V/I R=11/.05 R=220 Ohms
GRAPHS AND ANALYSIS
The graph above shows the relationship between potential difference and current. Our resistors form the two linear graphs thus they have a linear relationship and can be identified as Ohmic materials. The non-ohmic materials form the two non-linear graphs. They do not follow a direct relationship.
DISCUSSION QUESTIONS 1. In terms of experimental data, how is resistance defined and what are its units?
Resistance is defined by voltage divided by flow rate. It is measured in Ohms. 2. . Imagine that you had a third resistor that has a much smaller resistance than the ones used in the lab activity -Sketch a graph of pressure difference vs. flow rate that shows your 2 original resistors and this new resistor (sketch them on the same axes). Clearly label the lines. -Explain why you drew it this way.
The slope of the line represents the resistance. -How would the flow rate through this resistor change as the pressure difference decreases? Due to the linear relationship, it would decrease as well. 3. Assume that resistor A has 10 times the resistance of resistor B. What would a graph of resistance vs. current look like for these two resistors (sketch them on the same axes)? What about a graph of resistance vs. voltage? Justify your answers. Examine the graph of electric pressure difference vs. flow rate on the right. 4. Is this resistor Ohmic or non-Ohmic? Ohmic 5. What is the resistance of the object from which this data was collected? (Show your work.) R = V/I R = 5/1 R = 5 Ohms
CONCLUSION
This experiment proved my hypothesis correct. The data found shows the linear relationship expressed by Ohm's Law (V=IR). It also proves that the bulbs that were Ohmic obey Ohm's law due to their linear patterned graph. In addition it proves that the bulbs that were non-Ohmic do not obey Ohm's law due to their non linear patterned graph. Although our percent error was very large, given the range of the resistors the error actually recognizes good results. However, the error for the two bulbs was extremely large. This error could have come from the inaccuracy of the measure devices. The device may have given the wrong reading or have been off by decimal points. To address this error in the future I would use a more accurate device with readings that went much farther then one or two decimals.
Lab: Kirchoff's Rule
PURPOSE How do currents split in multi-loop circuits?
HYPOTHESIS W/ RATIONALE In a multi-loop circuit, currents will split at junctions dividing into two paths and therefore decreasing flow rate.
PROCEDURE Equipment: resistors, wire leads, D-cell batteries, several digital multimeters, 2 power supplies, 3 - 4 resistors, connecting wires Set-Up and Methods 1. Draw schematic diagram for each circuit 2. Using the Multimeter measure voltage and current at each resistor 3. Calculate theoretical values for each circuit DATA AND SAMPLE CALCULATIONS Circuit A
Circuit B
Circuit C
Circuit D ANALYSIS PERCENT ERROR
DISCUSSION QUESTIONS
1. Are the experimental values of the currents for the entire laboratory generally larger or smaller than the theoretical values expected for the currents? The experimental values of the currents for the entire laboratory are generally larger than the theoretical values expected for the currents.
2. It was pointed out in the laboratory that some error might be caused by neglect of the internal resistance of the emf. Would the internal resistance cause an error in the direction shown in your answer to question 1? State your reasoning for the direction of any error caused by the internal resistance. No, internal resistance would only lower the experimental values. It would never increase the values and therefore it would not cause error in the direction shown in answer 1. This is supported by the Ohm's law equation V=IR.
3. An ideal ammeter has zero resistance. Real ammeters have small but finite resistance. Would ammeter resistance cause an error in the proper direction to account for the direction of your error indicated in question 1? State your reasoning. No, this can also be supported by the Ohm's law equation. Increasing the resistance will only decrease the voltage.
4. The connecting wires in the experiment are assumed to have no resistance, but in fact have a finite resistance. Would this error be in the proper direction to account for the direction of the error stated in your answer to question 1? State your reasoning.
No, this can also be supported by the Ohm's law equation. Increasing the resistance will only decrease the voltage.
5. What is the meaning of any current values obtained in your solutions that are negative? Any value obtained in my solutions that are negative have no significance. The signs in front of the values are completely relative to the individual performing the equations. I could have solved for a value one way while another solved a different way. Our values would be the same however each would include opposite signs.
CONCLUSION
My original belief that as charges split at a junction, flow rate decreases was incorrect. As charges split at a junction, the flow rate actually increases because there is now less charge to occupy each wire. This explains the equations for solving for current at junctions. For example, if the original current, I1, splits off into I2 and I3 an equation would then become I1 = I2 + I3. This is because although there is no new charges entering the loop, it is simply one wire branching off into two and splitting up its charge. This can be seen through all experimental and theoretical values. Although my data proves this theory correct, there was an immense amount of error. Although some were very accurate, a great amount had percent errors as high as 38.75%. This error could have come from a number of issues. The greatest however was the readings produced by the multimeters. It was extremely difficult applying the right amount of pressure and taking the value at the same time for each reading. Thus, many many values could have been drastically off! In order to get more accurate results, more advanced technology would have to be used in order to get proper readings.
Chapter 20: Quantitative Analysis of Electric Circuits (Part 3)
Table of Contents
Lab: Ohm's Law
PURPOSEWhat is the relationship between Pressure Difference and Flow Rate?
What is the difference between Ohmic and Non-Ohmic materials?
HYPOTHESIS W/ RATIONALE
The pressure difference and flow rate have a direct relationship. I believe this because Ohm's Law includes the equation V=IR. Ohmic materials will follow Ohm's law while non-ohmic materials will not.
PROCEDURE
Available materials: variable power supply, batteries/holders, long bulb and socket, assorted resistors, multimeters, lead wires
General Set-up:
Measure voltage and current in circuit displayed below using multimeter and different resistors
DATA
SAMPLE CALCULATIONS
R=V/I
R=11/.05
R=220 Ohms
GRAPHS AND ANALYSIS
The graph above shows the relationship between potential difference and current. Our resistors form the two linear graphs thus they have a linear relationship and can be identified as Ohmic materials. The non-ohmic materials form the two non-linear graphs. They do not follow a direct relationship.
DISCUSSION QUESTIONS
1. In terms of experimental data, how is resistance defined and what are its units?
Resistance is defined by voltage divided by flow rate. It is measured in Ohms.
2. . Imagine that you had a third resistor that has a much smaller resistance than the ones used in the lab activity
-Sketch a graph of pressure difference vs. flow rate that shows your 2 original resistors and this new resistor (sketch them on the same axes). Clearly label the lines.
-Explain why you drew it this way.
The slope of the line represents the resistance.
-How would the flow rate through this resistor change as the pressure difference decreases?
Due to the linear relationship, it would decrease as well.
3. Assume that resistor A has 10 times the resistance of resistor B. What would a graph of resistance vs. current look like for these two resistors (sketch them on the same axes)? What about a graph of resistance vs. voltage? Justify your answers.
Examine the graph of electric pressure difference vs. flow rate on the right.
4. Is this resistor Ohmic or non-Ohmic? Ohmic
5. What is the resistance of the object from which this data was collected? (Show your work.)
R = V/I
R = 5/1
R = 5 Ohms
CONCLUSION
This experiment proved my hypothesis correct. The data found shows the linear relationship expressed by Ohm's Law (V=IR). It also proves that the bulbs that were Ohmic obey Ohm's law due to their linear patterned graph. In addition it proves that the bulbs that were non-Ohmic do not obey Ohm's law due to their non linear patterned graph. Although our percent error was very large, given the range of the resistors the error actually recognizes good results. However, the error for the two bulbs was extremely large. This error could have come from the inaccuracy of the measure devices. The device may have given the wrong reading or have been off by decimal points. To address this error in the future I would use a more accurate device with readings that went much farther then one or two decimals.
Lab: Kirchoff's Rule
PURPOSEHow do currents split in multi-loop circuits?
HYPOTHESIS W/ RATIONALE
In a multi-loop circuit, currents will split at junctions dividing into two paths and therefore decreasing flow rate.
PROCEDURE
Equipment: resistors, wire leads, D-cell batteries, several digital multimeters, 2 power supplies, 3 - 4 resistors, connecting wires
Set-Up and Methods
1. Draw schematic diagram for each circuit
2. Using the Multimeter measure voltage and current at each resistor
3. Calculate theoretical values for each circuit
DATA AND SAMPLE CALCULATIONS
Circuit A
Circuit B
Circuit C
Circuit D
ANALYSIS
PERCENT ERROR
DISCUSSION QUESTIONS
1. Are the experimental values of the currents for the entire laboratory generally larger or smaller than the theoretical values expected for the currents? The experimental values of the currents for the entire laboratory are generally larger than the theoretical values expected for the currents.
2. It was pointed out in the laboratory that some error might be caused by neglect of the internal resistance of the emf. Would the internal resistance cause an error in the direction shown in your answer to question 1? State your reasoning for the direction of any error caused by the internal resistance. No, internal resistance would only lower the experimental values. It would never increase the values and therefore it would not cause error in the direction shown in answer 1. This is supported by the Ohm's law equation V=IR.
3. An ideal ammeter has zero resistance. Real ammeters have small but finite resistance. Would ammeter resistance cause an error in the proper direction to account for the direction of your error indicated in question 1? State your reasoning. No, this can also be supported by the Ohm's law equation. Increasing the resistance will only decrease the voltage.
4. The connecting wires in the experiment are assumed to have no resistance, but in fact have a finite resistance. Would this error be in the proper direction to account for the direction of the error stated in your answer to question 1? State your reasoning.
No, this can also be supported by the Ohm's law equation. Increasing the resistance will only decrease the voltage.
5. What is the meaning of any current values obtained in your solutions that are negative? Any value obtained in my solutions that are negative have no significance. The signs in front of the values are completely relative to the individual performing the equations. I could have solved for a value one way while another solved a different way. Our values would be the same however each would include opposite signs.
CONCLUSION
My original belief that as charges split at a junction, flow rate decreases was incorrect. As charges split at a junction, the flow rate actually increases because there is now less charge to occupy each wire. This explains the equations for solving for current at junctions. For example, if the original current, I1, splits off into I2 and I3 an equation would then become I1 = I2 + I3. This is because although there is no new charges entering the loop, it is simply one wire branching off into two and splitting up its charge. This can be seen through all experimental and theoretical values. Although my data proves this theory correct, there was an immense amount of error. Although some were very accurate, a great amount had percent errors as high as 38.75%. This error could have come from a number of issues. The greatest however was the readings produced by the multimeters. It was extremely difficult applying the right amount of pressure and taking the value at the same time for each reading. Thus, many many values could have been drastically off! In order to get more accurate results, more advanced technology would have to be used in order to get proper readings.